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Isoperimetric clusters in homogeneous spaces via concentration compactness. / Novaga, Matteo; Paolini, Emanuele; Stepanov, Eugene; Tortorelli, Vincenzo.
в: Journal of Geometric Analysis, Том 32, № 11, 263, 11.2022.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Isoperimetric clusters in homogeneous spaces via concentration compactness
AU - Novaga, Matteo
AU - Paolini, Emanuele
AU - Stepanov, Eugene
AU - Tortorelli, Vincenzo
N1 - Novaga, M., Paolini, E., Stepanov, E. et al. Isoperimetric Clusters in Homogeneous Spaces via Concentration Compactness. J Geom Anal 32, 263 (2022). https://doi.org/10.1007/s12220-022-01009-8 Publisher Copyright: © 2022, Mathematica Josephina, Inc.
PY - 2022/11
Y1 - 2022/11
N2 - We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving homeomorphisms, for a quite wide range of perimeter functionals. Such generalized clusters are a natural “relaxed” version of a cluster and can be thought of as “albums” with possibly infinite pages, having a minimal cluster drawn on each page, the total perimeter and the vector of masses being calculated by summation over all pages, the total perimeter being minimal among all generalized clusters with the same masses. The examples include any anisotropic perimeter in a Euclidean space, as well as a hyperbolic plane with the Riemannian perimeter and Heisenberg groups with a canonical left invariant perimeter or its equivalent versions.
AB - We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving homeomorphisms, for a quite wide range of perimeter functionals. Such generalized clusters are a natural “relaxed” version of a cluster and can be thought of as “albums” with possibly infinite pages, having a minimal cluster drawn on each page, the total perimeter and the vector of masses being calculated by summation over all pages, the total perimeter being minimal among all generalized clusters with the same masses. The examples include any anisotropic perimeter in a Euclidean space, as well as a hyperbolic plane with the Riemannian perimeter and Heisenberg groups with a canonical left invariant perimeter or its equivalent versions.
KW - Primary 53C65
KW - Secondary 49Q15
KW - 60H05
KW - Isoperimetric sets
KW - Homogeneous space
KW - Isoperimetric clusters
UR - https://link.springer.com/article/10.1007/s12220-022-01009-8
UR - http://www.scopus.com/inward/record.url?scp=85136501872&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/3de5641c-6221-3438-8696-81e6c7f6fa23/
U2 - 10.1007/s12220-022-01009-8
DO - 10.1007/s12220-022-01009-8
M3 - Article
VL - 32
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
SN - 1050-6926
IS - 11
M1 - 263
ER -
ID: 100611857